The enhanced curvature perturbation may become a source for the tensor perturbation at the nonlinear order [1]}, [2]}, [3]}, [4]}. See also Refs. [5]}, [6]}, [7]}, [8]}, [9]}. It is due to the fact that the scalar mode and the tensor mode couple to each other at the second order in perturbations.
To study the tensor perturbation induced by the second-order scalar perturbation, we work in the conformal Newtonian gauge For the issue of gauge dependence, see e.g., Refs. [10]}, [11]}, [12]}, [13]}, [14]}., where the metric is given by
\(ds^2 = -(1+2\Phi )dt^2 + a^2\left[(1-2\Psi )\delta _{ij} + \frac{1}{2}h_{ij}\right]dx^i dx^j\,,\) 
